The CEO of the company that offers no-fuss car rentals by the hour, and which was taken over this week by Avis, told CNBC about a new plan to get around the yearly $50 to $60.

"What we're trying to do is make trial of our service much easier," Scott Griffith told "Squawk on the Street." The Access Plan is in a trial phase in Toronto and Vancouver, and is only available on weekdays.

Griffith said the program targets new customers and member retention, and that fees aren't going away. "Fees are an important part of our model. We have the leading brand, the best technology, and we make an easy upgrade path to go to the weekend — you just pay the fee and get in on the weekend."

The car-sharing company with some 760,000 members — largely big-city dwellers and college students — sold to car rental giant Avis for some $500 million, a fraction of its $1.2 billion valuation on the first day of its IPO in April 2011.

Griffith said the deal reflects an acceleration of competition and change in the sector, and that partnering with Avis would provide customers better options for personal mobility.

He said he expects Avis to leave Zipcar as a standalone subsidiary, and that pricing and practices will remain largely unchanged. "I believe we'll get to call our own shots," he said.

Zipcar has blazed a new trail in personal transportation since its founding in 2000, but it struggled to prove itself a profitable business with growth potential.

Zipcar's stock — which once dropped more than 75 percent off 2011 highs — popped up almost 50 percent since the takeover deal was announced. Avis' shares are up nearly 10 percent since the announcement.